There is no chance of any legal action working here as it's well out of copyright as that expires 70 years after the death of the creator and Conan Doyle died in 1930. There are several already existing and potentially conflicting trademarks on the Sherlock Holmes name in the UK (43 in in total for the name Sherlock) none of which would appear to prevent the current production continuing.

US law is different but cannot affect productions in the UK it is just possible she could block temporarily broadcast in America but I doubt she would want to actually go to court in case she is shown not to have legal title after all. This is the same sort of position as the patent trolls blighting the electronics hardware and software industry, they hope you will just pay up to avoid a court case but if forced into defending their position they often back down.